Multiple Input Multiple Output (MIMO) is one form of radio communication. According to MIMO, different signals are sent in parallel from a plurality of sending antennas and are spatially multiplexed, for example, for high-speed transmission.
In a radio communication system based on MIMO, a receiver side performs various detection processing for demultiplexing signals sent from the sending antenna as accurately as possible to detect the sent signals.
Full-Maximum Likelihood Detection (MLD) is one example of the detection processing. In Full-MLD, the distances between a receiving signal point and sending candidate points (or signal replica candidate points) may be acquired to estimate the sending candidate point with the shortest distance as the sending signal point, for example. However, Full-MLD computes distances for all sending candidate points, an enormous amount of computing is required with some number of sending antennas or some modulation methods. Accordingly, sending signal detection processing called QRM-MLD may have been used in the past.
QRM-MLD is a combination of QR decomposition and MLD, for example, and estimates a sending signal point while reducing (or concentrating) the number of sending candidate points. Thus, QRM-MLD requires less amount of computing than Full-MLD. QRM-MLD will be described below.
First of all, a radio communication system based on MIMO may be modeled, for example, as the following Expression (1).y=Hx+n  (1)
In Expression (1), y is a receiving signal vector, x is a sending signal vector, n is a noise vector, and H is a channel response matrix (or channel matrix). If “2” sending antennas and “2” receiving antennas are available,
                              (                                                                      y                  0                                                                                                      y                  1                                                              )                =                                            (                                                                    a                                                        b                                                                                        c                                                        d                                                              )                        ⁢                          (                                                                                          x                      0                                                                                                                                  x                      1                                                                                  )                                +                      (                                                                                n                    0                                                                                                                    n                    1                                                                        )                                              (        2        )            
Expression (1) may be expressed as the following Expression (2).
In Expression (2), y0 and y1 are receiving signal points, x0 and x1 are sending signal points (or sending signal candidate points), a, b, c, and d are components of the channel matrix H, and n0 and n1 are components of noise.
Here, the channel matrix H may be decomposed into a unitary matrix Q (whose matrix product with a complex conjugate transposition matrix Q* is equal to a unit matrix) and a higher triangular matrix R and may be expressed as the following Expression (3).H=QR  (3)
(QR Decomposition).
Multiplying both sides of Expression (2) by the complex conjugate transposition matrix Q* of the unitary matrix Q from the left side, the following Expression (4) may be acquired.
                                                                                          Q                  *                                ⁢                y                            =                                                Q                  *                                ⁡                                  (                                      Hx                    +                    n                                    )                                                                                                        =                                                                    Q                    *                                    ⁢                  Hx                                +                                                      Q                    *                                    ⁢                  n                                                                                                        =                              Rx                +                                  n                  ′                                                                                        (        4        )            
Thus, Expression (4) may be expressed as the following Expression (5).
                              (                                                                      y                  0                  ′                                                                                                      y                  1                  ′                                                              )                =                                            (                                                                                          a                      ′                                                                                                  b                      ′                                                                                                            0                                                                              c                      ′                                                                                  )                        ⁢                          (                                                                                          x                      0                                                                                                                                  x                      1                                                                                  )                                +                      (                                                                                n                    0                    ′                                                                                                                    n                    1                    ′                                                                        )                                              (        5        )            
Here, y0′ and y1′ are points acquired by multiplying receiving signal points y0 and y1 by the unitary matrix Q; a′, b′, and c′ are components of the higher triangular matrix R, and n0′ and n1′ are values acquired by multiplying noise components n0 and n1 by the unitary matrix Q. The components of Expression (5) are:y0′=a′x0+b′x1+n0′  Expression (5-1)y1′=c′x1+n1′  Expression (5-2)
QRM-MLD selects candidate points with the lowest noise from the candidate points x0 and x1, that is, x0 and x1 with the lowest result (MLD) of:|y1′−c′x1|2+|y0′−a′x0−b′x1|2  Expression (5-3)
In other words, in a first stage, a plurality of candidate points x1 with |y1′−c′x1|2 that is lower than a threshold value are selected, and |y1′−c′x1|2 is then calculated. In a second stage, the candidate point x0 with the lowest |y0′−a′x0−b′x1|2 is selected from a plurality of candidate points x1 selected in the first stage, and |y0′−a′x0−b′x1|2 is calculated. Finally, the candidate point with the lowest result of Expression (5-3) is selected from the selected candidate points x0 and x1, and the selected candidate point is determined (or estimated) as the sending signal point.
Hitherto, the detection of a sending signal with QRM-MLD includes dividing a channel matrix into a plurality of submatrices and using the inverse matrices of the submatrices for QR decomposition to reduce the amount of processing.